The Quantum McKay Correspondence for polyhedral singularities

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the crepant resolution conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold resolution clarified. Version to appear in Inventione

Patients' preferences for the management of non-metastatic prostate cancer: discrete choice experiment

Objective To establish which attributes of conservative treatments for prostate cancer are most important to men. Design Discrete choice experiment. Setting Two London hospitals. Participants 129 men with non-metastatic prostate cancer, mean age 70 years; 69 of 118 (58%) with T stage 1 or 2 cancer at diagnosis. Main outcome measures Men's preferences for, and trade-offs between, the attributes of diarrhoea, hot flushes, ability to maintain an erection, breast swelling or tenderness, physical energy, sex drive, life expectancy, and out of pocket expenses. Results The men's responses to changes in attributes were all statistically significant. When asked to assume a starting life expectancy of five years, the men were willing to make trade-offs between life expectancy and side effects. On average, they were most willing to give up life expectancy to avoid limitations in physical energy (mean three months) and least willing to trade life expectancy to avoid hot flushes (mean 0.6 months to move from a moderate to mild level or from mild to none). Conclusions Men with prostate cancer are willing to participate in a relatively complex exercise that weighs up the advantages and disadvantages of various conservative treatments for their condition. They were willing to trade off some life expectancy to be relieved of the burden of troublesome side effects such as limitations in physical energy

The Globular Cluster Luminosity Function and Specific Frequency in Dwarf Elliptical Galaxies

The globular cluster luminosity function, specific globular cluster frequency, S_N, specific globular cluster mass, T_MP, and globular cluster mass fraction in dwarf elliptical galaxies are explored using the full 69 galaxy sample of the HST WFPC2 Dwarf Elliptical Galaxy Snapshot Survey. The GCLFs of the dEs are well-represented with a t_5 function with a peak at M_{V,Z}^0(dE,HST) = -7.3 +/- 0.1. This is ~0.3 magnitudes fainter than the GCLF peaks in giant spiral and elliptical galaxies, but the results are consistent within the uncertainties. The bright-end slope of the luminosity distribution has a power-law form with slope alpha = -1.9 +/- 0.1. The trend of increasing S_N or T_MP with decreasing host galaxy luminosity is confirmed. The mean value for T_MP in dE,N galaxies is about a factor of two higher than the mean value for non-nucleated galaxies and the distributions of T_MP in dE,N and dE,noN galaxies are statistically different. These data are combined with results from the literature for a wide range of galaxy types and environments. At low host galaxy masses the distribution of T_MP for dE,noN and dI galaxies are similar. This supports the idea that one pathway for forming dE,noN galaxies is by the stripping of dIs. The formation of nuclei and the larger values of T_MP in dE,N galaxies may be due to higher star formation rates and star cluster formation efficiencies due to interactions in galaxy cluster environments.Comment: 53 pages, 13 figures, 12 tables, accepted by the Astrophysical Journa

The Theatre of Punishment: Case Studies in the Political Function of Corporal and Capital Punishment

Michel Foucault famously argued that punishment was an expression of power—a way for the State to shore up and legitimize its political authority. Foucault attributed the historical shift away from public torture and corporal punishment, which occurred during the 19th century, to the availability of new techniques of social control; however, corporal and capital punishment (what we term “shock punishment”) persists in many penal systems to this day, suggesting that these countries have for some reason not fully undergone this penal evolution. Using the experiences of Hong Kong and Singapore as case studies, we attempt to explain why this is the case. We argue that, while a range of factors contribute to why countries employ shock punishment, retention is often linked to the political stability of a government’s rule. Punishment, as a visceral expression of power, makes shock punishment particularly appealing to States grappling with political insecurity. In the post-war period, Hong Kong’s colonial government did not feel their rule challenged to the same extent as the newly independent government in Singapore. The result is two radically divergent stories with regards to corporal punishment, with Hong Kong abolishing the practice altogether in 1991 and Singapore not only retaining it, but greatly expanding its usage. As further support for our thesis, we offer empirical data regarding the use of shock punishment and the political freedom of the societies that retain it. We identify a fairly robust, positive correlation between the use of shock punishment and authoritarian and semi-authoritarian governments desperate to legitimize their rule. The final conclusion we reach is that, while many factors undoubtedly contribute to the retention of shock punishment, its expressive power plays a significant role in why many States continue to employ it

In vivo nuclear magnetic resonance imaging

A number of physiological changes have been demonstrated in bone, muscle and blood after exposure of humans and animals to microgravity. Determining mechanisms and the development of effective countermeasures for long duration space missions is an important NASA goal. The advent of tomographic nuclear magnetic resonance imaging (NMR or MRI) gives NASA a way to greatly extend early studies of this phenomena in ways not previously possible; NMR is also noninvasive and safe. NMR provides both superb anatomical images for volume assessments of individual organs and quantification of chemical/physical changes induced in the examined tissues. The feasibility of NMR as a tool for human physiological research as it is affected by microgravity is demonstrated. The animal studies employed the rear limb suspended rat as a model of mucle atrophy that results from microgravity. And bedrest of normal male subjects was used to simulate the effects of microgravity on bone and muscle

Correlation of missions 191, 51M and helicopter photography

The data obtained during aerial photography flights using a helicopter are presented. The areas photographed are identified as three areas within Test Site 175: (1) Rosenberg, (2) Houston Ship Channel/Trinity Bay, and (3) the Somerville Dam. Data are presented in the form of charts. Reproductions of the aerial photographs are included

Chen-Ruan cohomology of ADE singularities

We study Ruan's \textit{cohomological crepant resolution conjecture} for orbifolds with transversal ADE singularities. In the $A_n$-case we compute both the Chen-Ruan cohomology ring $H^*_{\rm CR}([Y])$ and the quantum corrected cohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the later up to some additional, technical assumptions. We construct an explicit isomorphism between $H^*_{\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case, verifying Ruan's conjecture. In the $A_n$-case, the family $H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that the conjecture should be slightly modified. We propose a new conjecture in the $A_n$-case which we prove in the $A_2$-case by constructing an explicit isomorphism.Comment: This is a short version of my Ph.D. Thesis math.AG/0510528. Version 2: chapters 2,3,4 and 5 has been rewritten using the language of groupoids; a link with the classical McKay correpondence is given. International Journal of Mathematics (to appear

Interactional Structure Applied to the Identification and Generation of Visual Interactive Behavior: Robots that (Usually) Follow the Rules

Peer reviewe